This magnificent book is the first comprehensive history of statistics from its beginnings around 1700 to its emergence as a distinct and mature discipline around 1900. Stephen M. Stigler shows how statistics arose from the interplay of mathematical concepts and the needs of several applied sciences including astronomy, geodesy, experimental psychology, genetics, and sociology. He addresses many intriguing questions: How did scientists learn to combine measurements made under different conditions? And how were they led to use probability theory to measure the accuracy of the result? Why were statistical methods used successfully in astronomy long before they began to play a significant role in the social sciences? How could the introduction of least squares predate the discovery of regression by more than eighty years? On what grounds can the major works of men such as Bernoulli, De Moivre, Bayes, Quetelet, and Lexis be considered partial failures, while those of Laplace, Galton, Edgeworth, Pearson, and Yule are counted as successes? How did Galtons probability machine (the quincunx) provide him with the key to the major advance of the last half of the nineteenth century?
Stiglers emphasis is upon how, when, and where the methods of probability theory were developed for measuring uncertainty in experimental and observational science, for reducing uncertainty, and as a conceptual framework for quantitative studies in the social sciences. He describes with care the scientific context in which the different methods evolved and identifies the problems (conceptual or mathematical) that retarded the growth of mathematical statistics and the conceptual developments that permitted major breakthroughs.
Statisticians, historians of science, and social and behavioral scientists will gain from this book a deeper understanding of the use of statistical methods and a better grasp of the promise and limitations of such techniques. The product of ten years of research, The History of Statistics will appeal to all who are interested in the humanistic study of science.
Introduction
I. The Development of Mathematical Statistics in Astronomy and Geodesy before 1827
1. Least Squares and the Combination of Observations
Legendre in 1805
Cotess Rule
Tobias Mayer and the Libration of the Moon
Saturn, Jupiter, and Euler
Laplaces Rescue of the Solar System
Roger Boscovich and the Figure of the Earth
Laplace and the Method of Situation
Legendre and the Invention of Least Squares
2. Probabilists and the Measurement of Uncertainty
Jacob Bernoulli
De Moivre and the Expanded Binomial
Bernoullis Failure
De Moivres Approximation
De Moivres Deficiency
Simpson and Bayes
Simpsons Crucial Step toward Error
A Bayesian Critique
3. Inverse Probability
Laplace and Inverse Probability
The Choice of Means
The Deduction of a Curve of Errors in 1772-1774
The Genesis of Inverse Probability
Laplaces Memoirs of 1777-1781
The Error Curve of 1777
Bayes and the Binomial
Laplace the Analyst
Nonuniform Prior Distributions
The Central Limit Theorem
The Gauss-Laplace Synthesis
Gauss in 1809
Reenter Laplace
A Relative Maturity: Laplace and the Tides of the Atmosphere
The Situation in 1827
II. The Struggle to Extend a Calculus of Probabilities to the Social Sciences
5. Quetelets Two Attempts
The de Keverberg Dilemma
The Average Man
The Analysis of Conviction Rates
Poisson and the Law of Large Numbers
Poisson and Juries
Comte and Poinsot
Cournots Critique
The Hypothesis of Elementary Errors
The Fitting of Distributions: Quetelismus
6. Attempts to Revive the Binomial
Lexis and Binomial Dispersion
Arbuthnot and the Sex Ratio at Birth
Buckle and Campbell
The Dispersion of Series
Lexiss Analysis and Interpretation
Why Lexis Failed
Lexian Dispersion after Lexis
7. Psychophysics as a Counterpoint
The Personal Equation
Fechner and the Method of Right and Wrong Cases
Ebbinghaus and Memory
III. A Breakthrough in Studies of Heredity
8. The English Breakthrough: Galton
Galton, Edgeworth, Pearson
Galtons Hereditary Genius and the Statistical Scale
Conditions for Normality
The Quincunx and a Breakthrough
Reversion
Symmetric Studies of Stature
Data on Brothers
Estimating Variance Components
Galtons Use of Regression
Correlation
9. The Next Generation: Edgeworth
The Critics Reactions to Galtons Work
Pearsons Initial Response
Francis Ysidro Edgeworth
Edgeworths Early Work in Statistics
The Link with Galton
Edgeworth, Regression, and Correlation
Estimating Correlation Coefficients
Edgeworths Theorem
10. Pearson and Yule
Pearson the Statistician
Skew Curves
The Pearson Family of Curves
Pearson versus Edgeworth
Pearson and Correlation
Yule, the Poor Law, and Least Squares: The Second Synthesis
The Situation in 1900
Appendix A. Syllabus for Edgeworths 1885 Lectures
Appendix B. Syllabus for Edgeworths 1892 Newmarch Lectures
Suggested Readings
Bibliography
Index
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